论文标题
耦合分析用于耦合对流扩散反应问题的计算
Convergence Analysis for Computation of Coupled Advection-Diffusion-Reaction Problems
论文作者
论文摘要
对耦合对流扩散反应方程的计算的收敛性进行了研究。在计算中，具有不同系数甚至类型的方程式在两个子域中分配，并且在从时间级到下一个方程式进行时，在方程式之间进行了Schwarz迭代。分析始于由显式方程完全离散化的线性系统。得出了收敛的条件，并讨论了方程中的速度和差异的影响。然后，它进入隐式方案，并得出收敛速度的递归表达。获得了Schwarz迭代的最佳界面条件，并导致“完美收敛”，即在迭代两次之内收敛。此外，方法和分析扩展到粘性汉堡方程的耦合。数值实验表明，在线性情况下绘制的结论，例如“完美收敛”，可能保留在汉堡方程计算中。
A study is presented on the convergence of the computation of coupled advection-diffusion-reaction equations. In the computation, the equations with different coefficients and even types are assigned in two subdomains, and Schwarz iteration is made between the equations when marching from a time level to the next one. The analysis starts with the linear systems resulting from the full discretization of the equations by explicit schemes. Conditions for convergence are derived, and its speedup and the effects of difference in the equations are discussed. Then, it proceeds to an implicit scheme, and a recursive expression for convergence speed is derived. An optimal interface condition for the Schwarz iteration is obtained, and it leads to "perfect convergence", that is, convergence within two times of iteration. Furthermore, the methods and analyses are extended to the coupling of the viscous Burgers equations. Numerical experiments indicate that the conclusions, such as the "perfect convergence, " drawn in the linear situations may remain in the Burgers equations' computation.
